Alexander Craig Aitken

Alec Aitken left the Otago Boys' High School in Dunedin in 1913 having won a scholarship to Otago University. He began to study languages and mathematics with the intention of becoming a school teacher but his university career was interrupted by World War I.

He enlisted in 1915 and served in Gallipoli, Egypt and France being wounded at the battle of the Somme. His war experiences were to haunt him for the rest of his life. After three months in hospital he was sent back to New Zealand in 1917. The following year he returned to his university studies graduating in 1920 with First Class Honours in French and Latin but only Second Class in mathematics in which he had no proper instruction.

Aitken followed his original intention and became a school teacher at his old school Otago Boys' High School. His mathematical genius bubbled under the surface and, encouraged by the new professor of mathematics at Otago University, Aitken came to Scotland in 1923 and studied for a Ph.D. at Edinburgh under Whittaker. Rather remarkably his Ph.D. thesis was considered so outstanding that he was awarded a D.Sc. for it.

In 1925 he was appointed to Edinburgh where he spent the rest of his life. After holding lecturing posts in actuarial mathematics, then in statistics, then mathematical economics he became a Reader in statistics in 1936, the year he was elected a Fellow of the Royal Society. Ten years later he was appointed to Whittaker's chair.

Aitken had an incredible memory (he knew to 2000 places) and could instantly multiply, divide and take roots of large numbers. He describes his own mental processes in the article [3]. Although some may suggest this has little to do with mathematical ability Aitken himself wrote:-

Familiarity with numbers acquired by innate faculty sharpened by assiduous practice does give insight into the profounder theorems of algebra and analysis.

Aitken's mathematical work was in statistics, numerical analysis and algebra. In numerical analysis he introduced the idea of accelerating the convergence of a numerical method. He also introduced a method of progressive linear interpolation. In algebra he made contributions to the theory of determinants. He also saw clearly how invariant theory came under the theory of groups but wrote that he had never followed through his ideas because of

various circumstances of anxiety, or duty, or bad health ... I have observed my talented younger contemporary Dudley Littlewood assault and capture most of this terrain.

Aitken wrote several books The theory of canonical matrices (1932) was written jointly with Turnbull. With Rutherford he was editor of a series of the University Mathematical Texts and himself wrote Determinants and matrices (1939) and Statistical Mathematics (1939).

In [2], describing his period of recovery from a small operation in 1934 Aitken writes:-

The nights were bad, in the daytime colleagues and other friends visited me, and I tried to think about abstract things, such as the theory of probability and the theory of groups - and I did begin to see more deeply into these rather abstruse disciplines. Indeed I date a change in my interests and an increase in competence, from these weeks of enforced physical inactivity.

Also in [2] Aitken describes the reaction of other mathematicians to his work:-

... the papers on numerical analysis, statistical mathematics and the theory of the symmetric group continued to write themselves in steady succession, with other small notes on odds and ends. Those that I valued most, the algebraic ones, seemed to attrach hardly any notice, others, which I regarded as mere application of the highly compressed and powerful notation and algebra of matrices to standard problems in statistics or computation found great publicity in America...

A colleague at St Andrews was a student in Edinburgh in the early 1960's. He writes:-

Professor Aitken's first year mathematics lectures were rather unusual. The fifty minutes were composed of forty minutes of clear mathematics, five minutes of jokes and stories and five minutes of 'tricks'. For the latter Professor Aitken would ask for members of the class to give him numbers for which he would then write down the reciprocal, the square root, the cube root or other appropriate expression. From the five minutes of 'stories' one also recalls as part of his lectures on probability a rather stern warning about the evils and foolishness of gambling!

In fact Aitken's memory was also a problem for him. For most people memories fade in time which is particularly fortunate for the unpleasant things which happen. However with Aitken memories did not fade and his horrific memories of the battle of the Somme lived with him as real as the day he lived them. He wrote of them in [1] near the end of his life. These memories must have contributed to the ill health he suffered, and eventually led to his death.